3 of us have had the same identical problem with the same Cummins 4BT engine, same Cummins 4BT starter and same type of cheapo aftermarket ignition switch for a Dodge truck. I chose to leave the pushbutton, they didn't, and there's worked fine with a good quality HD diesel rated switch, so no other problem except excessive amperage draw as described. I assume mine would work fine with a HD diesel rated switch as well.

Diesels pull a whole bunch more ampreage than gassers and the switch was only rated for a gasser. If there was 'some other problem' I'd think it would have made itself obvious in the last 5-6 years since the Cummins install. Regardless, the pushbutton switch works fine when correctly wired.